1. **Stating the problem:** We have 5 onions and 4 potatoes, with 2 onions and 2 potatoes rotten. We want the probability that if two items are randomly picked, they are both either potatoes or both rotten. 2. **Total items:** Total items = 5 onions + 4 potatoes = 9. 3. **Total ways to pick 2 items:** Using combinations, total ways = $$\binom{9}{2} = \frac{9 \times 8}{2} = 36$$. 4. **Calculate ways to pick 2 potatoes:** There are 4 potatoes, so ways = $$\binom{4}{2} = \frac{4 \times 3}{2} = 6$$. 5. **Calculate ways to pick 2 rotten items:** Rotten items = 2 onions + 2 potatoes = 4 rotten items. Ways to pick 2 rotten = $$\binom{4}{2} = \frac{4 \times 3}{2} = 6$$. 6. **Calculate ways to pick 2 items that are both potatoes and rotten:** Rotten potatoes = 2. Ways to pick 2 rotten potatoes = $$\binom{2}{2} = 1$$. 7. **Use inclusion-exclusion principle:** Number of ways to pick 2 items that are both potatoes or both rotten = ways(potatoes) + ways(rotten) - ways(both potatoes and rotten) = $$6 + 6 - 1 = 11$$. 8. **Calculate probability:** $$P = \frac{11}{36}$$. **Final answer:** The probability that two randomly picked items are both potatoes or both rotten is $$\frac{11}{36}$$.